High School Session 1:Exploring the Critical Areas

Module 1:A Closer Look at the Common

Core State Standards for Mathematics

Expected Outcomes

• Participants will deepen their understanding of the structure of the CCSS for Mathematics and at least one suggested pathway course.

• Participants will deepen their understanding that the critical areas suggest a possible grouping of the standards into coherent blocks for each high school course.

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• Focus• Coherence• Clarity• Specificity

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Principle #1: Increases in student learning occur only as a consequence of improvements in the level of content, teachers’ knowledge and skill, and student engagement.

Richard Elmore, Ph.D., Harvard Graduate School of Education

Principle #2: If you change one element of the instructional core, you have to change the other two.

The Instructional Core

Adapted from the Public Education Leadership Project at Harvard University

STRUCTURES

POLICIES, PROCESSES & PROCEDURES

RESOURCES

HUMAN, MATERIAL, M

ONEY

STAKEHOLDERS

CULTURE

Organizational Elements

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The high school standards are listed within conceptual categories

CCSSM High SchoolConceptual Categories

• Number and Quantity (N)• Algebra (A)• Functions (F)• Modeling (*)• Geometry (G)• Statistics and Probability (S)

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CCSSM High SchoolConceptual Categories

• The big ideas that connect mathematics across high school

• A progression of increasing complexity• Description of the mathematical content to

be learned, elaborated through domains, clusters, and standards

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Domains

• Overarching “big ideas” that connect topics across the grades/courses

• Descriptions of the mathematical content to be learned, elaborated through clusters and standards

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Clusters of Standards

• Indicate WHAT students should know and be able to do

• May appear in multiple grade levels/courses with increasing developmental standards as the grade levels progress

• Reflect both mathematical understandings and skills, which are equally important

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Conceptual Category

Cluster Headings

Cluster Headings

Cluster Headings

Cluster Headings

DOMAIN

DOMAIN

DOMAIN

DOMAIN

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Algebra

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Domain

Cluster Headings

Standards

Conceptual Category

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Each course, outlined in the Pathways document is organized around Critical Areas (Units).

Traditional Pathway: High School Algebra I

Five critical areas in an Algebra I course

1. Relationships Between Quantities and Reasoning with Equations

2. Linear and Exponential Relationships3. Descriptive Statistics 4. Expressions and Equations5. Quadratic Functions and Modeling

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Task: Examining the Critical Areas

• What are the important mathematical ideas for this critical area?

• What types of evidence would convince you that a student understands these ideas?

• What common misconceptions do students have when studying these critical areas? What challenges have you had in teaching these areas?

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Whole group discussion

• What are the similarities in the types of evidence that would convince you that a student understands these ideas?

• Are there common themes in student misconceptions and in challenges to teaching?

• Compare the concepts in the critical areas with those that you are currently teaching. In general, how are they similar? How are they different?

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Reflection

• How do the critical areas help to bring focus to the standards for the course that you examined today?

• How will you use the critical areas to inform your curriculum and guide your instruction?

• What questions do you still have about the conceptual categories and critical areas?

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